Question: Simplify the following expression: $ q = \dfrac{-5x - 8}{8x - 2} - \dfrac{-7}{9} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{-5x - 8}{8x - 2} \times \dfrac{9}{9} = \dfrac{-45x - 72}{72x - 18} $ Multiply the second expression by $\dfrac{8x - 2}{8x - 2}$ $ \dfrac{-7}{9} \times \dfrac{8x - 2}{8x - 2} = \dfrac{-56x + 14}{72x - 18} $ Therefore $ q = \dfrac{-45x - 72}{72x - 18} - \dfrac{-56x + 14}{72x - 18} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-45x - 72 - (-56x + 14) }{72x - 18} $ Distribute the negative sign: $q = \dfrac{-45x - 72 + 56x - 14}{72x - 18}$ $q = \dfrac{11x - 86}{72x - 18}$